Method and system for scoring and ranking a plurality of relationships in components of socio-technical system

ABSTRACT

A method and system for scoring and ranking a plurality of component links in a social technical system having a plurality of components representing people and objects are provided. In one aspect, a degree of consistency relative to two or more people working on one or more objects and dependencies between the objects is determined to derive scores for the component links. The method and system identifies gaps in the link and determines the impact of filling the gaps. In another aspect, component links may be ranked and scores aggregated to provide system level quantifications.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to U.S. patent application Ser. No. ______,filed on May 18, 2007, entitled “A Method and System For UnderstandingSocial Organization in a Design and Development Process” (AttorneyDocket No. YOR920070151US1 (21029)), and having a common assignee, whichapplication is incorporated by reference herein in its entirety.

FIELD OF THE INVENTION

The present application relates to socio-technical systems in generaland, particularly to a method and system for analyzing existing andpotential link components in socio-technical systems and measuring theoverall consistency, based on a finite set of reference patterns.

BACKGROUND OF THE INVENTION

Socio-technical systems include social structures of actors or peopleand technical structures of products that people create with their work.A socio-technical software network is a combined model that representssoftware developers and their relationships, software artifacts (e.g.,design documents, packages, modules, classes, methods, error reports,etc.) and their relationships, linkage between developers and artifacts,and their attributes. Analyzing the importance of relationships, moregenerally known as linkages or links, in the model helps in describingthe extent of each link's importance with respect to the overallconsistency between the social structure and the technical productstructure. The term consistency refers to a more general form oforganizational congruence than referred to in e.g., (M. Cataldo, P. A.Wangstrom, J. D. Herbsleb, and K. M. Carley, “Identification ofCoordination Requirements: Implications for the Design of Collaborationand Awareness Tools”, in Proceedings of the Conference on ComputerSupported Cooperative Work (CSCW '06), Banff, Alberta, Canada, Nov. 4-8,2006, herein referred to as “Cataldo et al.”) or (Burton, R. M. andObel, B. Strategic Organizational Diagnosis and Design. Kluwer AcademicPublishers, Norwell, Mass., 1998, herein referred to as “Burton etal.”). These measurements can be used for system diagnosis, designand/or organizational optimization. For example, such analysis may beused to determine how well a particular organization is structured tohandle a particular project.

The measure of consistency addressed in the present disclosure extendswell beyond the notion of congruence, which is a measurementtraditionally considered in organizational design, see for example,Burton et al. The notion of consistency is based on a set ofidentifiable reference patterns within the network model of the socialtechnical system. Note that these patterns are specifically related torecognizable structural aspects of the network, as opposed toorganizational patterns (see, for example, “Organizational Patterns ofAgile Software Development” by James Coplien and Neil Harrison, PearsonPrentice Hall, 2005). While consistency is a measurement that addressesthe alignment of subnetworks that may be organized on different plane,note that it is not network (or graph) comparison of the type in theapproach by e.g., “Design Pattern Detection Using Similarity Scoring” byNikolaos Tsantalis, Alexander Chatzigeorgiou, George Stephanides, andSpyros T. Halkidis, IEEE Transactions On Software Engineering, Vol. 32,No. 11, November 2006.

Measurements may be determined that indicate how much the structure of adevelopment organization mirrors other aspects of the project such aswork items assigned to groups and individuals in the organization, andwork actually carried out in terms of software components developed bythe organization. Known solutions for determining such measurements usenon-analytical methods of comparison. Such non-analytical methods ofcomparison rely on subjective assessments and may be incomplete, anddifficult to automate. While a semi-analytical approach is described inCataldo et al., that methodology uses matrix algebra to compute acongruence metric and concerns tasks, however, but does not addressmeasuring importance of a given link, does not analyze the networkdirectly, and does not analyze components of the work product output bytasks. Further, both non-analytical and semi-analytical methods do notconsider detailed structure of the underlying components in thecomparison.

Therefore, an improved methodology, for example, which takes intoaccount various attributes and which can be automated is desirable.Further, it is desirable to have such methodology provide measurementsthat are time phased, for example, to determine how variations of levelof such measurements in time within the same project influenceperformance and quality. It is also desirable to have such methodologyprovide a measurement of importance at the component (link) level, aswell as a consistency measurement at the overall system level.

BRIEF SUMMARY OF THE INVENTION

A method and system for scoring a plurality of component links in asocio technical system are provided. The socio technical system maycomprise a plurality of components representing people and objects, theplurality of components links representing a plurality of relationshipsbetween the plurality of components. The method in one aspect maycomprising determining a measure of consistency relative to a network ofpeople components and a network of object components in a sociotechnical system, the network of people components including componentsrepresenting people and one or more links between the componentsrepresenting people, and the network of object components includingcomponents representing objects worked on by at least some of thecomponents representing people and one or more links between thecomponents representing objects. The method may also comprisedetermining a measure of contribution to the measure of consistency forone or more links between said components, based on presence or absenceof said one or more links in the social technical system. The measure ofcontribution and the measure of consistency can be used for analyzingand structuring work group in a project.

A system for scoring a plurality of component links in a socialtechnical system in one aspect may include means such as computerprocessor, module, and/or circuitry for providing the functionalitiesfor the above-described method.

Further features as well as the structure and operation of variousembodiments are described in detail below with reference to theaccompanying drawings. In the drawings, like reference numbers indicateidentical or functionally similar elements.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example of a socio-technical system modeled by anetwork.

FIG. 2 illustrates null case coordination with respect to a singleartifact.

FIG. 3 illustrates direct coordination with respect to a singleartifact.

FIG. 4 illustrates indirect coordination having path length two withrespect to a single artifact.

FIG. 5 illustrates indirect coordination having path length tree withrespect to a single artifact.

FIG. 6 illustrates singular coordination with respect to dependentartifacts.

FIG. 7 illustrates direct coordination with respect to dependentartifacts.

FIG. 8 illustrates indirect coordination, path length two, with respectto dependent artifacts.

FIG. 9 illustrates indirect coordination, path length three, withrespect to dependent artifacts.

FIG. 10 is a flow diagram illustrating a method of the presentdisclosure in one embodiment for finding measurements related tocollaboration patterns.

FIG. 11 is a flow diagram illustrating a method in one embodiment forfinding measurements related to coordination patterns.

FIG. 12 illustrates an example set of reference patterns, relating tocoordination, collaboration patterns and anti-patterns.

DETAILED DESCRIPTION

A method and system of the present disclosure in one embodiment measuresrelationships or coordination by comparing an abstract graph model ofsocial structures of people (also referred to as a “social network”)with an abstract graph representation of the technical structure of thework product. The comparison is facilitated through the use of “joins”between the two graph that identify connections between node entities inthe social graph with node entities in the technical graph. The methodand system of the present disclosure in one embodiment considers one ormore aspects of mutual existing structural components as well as mutualnon-existence of structural components in the resulting metric. Themethod and system of the present disclosure in one embodiment providesthe flexibility for calibrating the measurement to reflect keyrequirements of measurement interest in the environment and application.

Models of socio-structure and technical-structure and joins arerepresented electronically. A method and system of the presentdisclosure in one embodiment automatically computes measurement ofrelationships joins) from the socio-structure and technical-structuremodels. For instance, given two graphs and a set of joins between them,a measurement may be provide, for example, on a scale of 0 to 1, todescribe how “consistent” they are. Other measurements may includepredicting the existence of arcs in a graph that does not have fullinformation.

FIG. 1 illustrates an example of a socio-technical system modeled as anetwork. The method and system in one embodiment observes thecoordination patterns in the system, and determines and interpretsmeasurements based on the patterns.

The following notation is used by the model:

n:=The number of people involved in the socio-technical systemP:=The set of people, indexed p₁, p₂, . . . , p_(n). That is, P={p₁, p₂,. . . , p_(n)}.Ep:=The edges between people nodes, i.e., (p_(i), p_(j))∈Ep indicatesthere is a work relationship between person pi and person pj, where pi,pj∈P. Note that in this model, the elements of Ep are unordered pairs.That is (p_(i), p_(j))=(p_(j), p_(i)).Gp (P,Ep):=The graph with node set P and link set Ep, representing thesocial network aspect of the model.m:=The number of work product artifacts involved in the socio technicalsystemS:=The set of work product artifacts, indexed s₁, s₂, . . . , s_(m).That is, S={s₁, s₂, . . . , s_(m)}.As:=The dependencies between work products, i.e., (s_(i), s_(j))∈Asindicates there is a dependency by artifact s_(j) on artifact s_(i),where s_(i), s_(j)∈S.Gs(S, As):=The graph with node set S and link set As, representing thework product aspect of the model.J:=The set of “joins” in the socio-technical system. These are directedlinks from people nodes to work product nodes. That is, (p, s)∈Jindicates that there is a defined relationship by an assignment ofperson p∈P to work product artifact s∈S.

The social network model shown in FIG. 1 is an undirected graph Gp(P,Ep)102 and the technical artifact dependency model is a directed graphGs(S, As) 104. However, the method and system of the present disclosurealso may be applied to directed graphs for people. Conceptually orlogically, the socio plane 102 may include components or nodesrepresenting people and links or relationships between the components ornodes representing people, for example, forming a network of peoplecomponents. Examples of relationships between people may include but arenot limited to communication, trust, organizational connection, etc. Thetechnical plane 104 may include components or nodes representingartifacts or objects worked on by people and dependencies orrelationships between the artifacts represented by one or more links,for example, forming a network of object components.

FIG. 2 illustrates null case coordination with respect to a singleartifact. That is, the graph shows one person 202 or actor associatedwith (or working on) 206 one artifact (a product or a component of aproduct) 204.

FIG. 3 illustrates direct coordination with respect to a singleartifact. When two people are both assigned to the same work artifact,they are expected to coordinate in their communications. FIG. 3 shows anexample of a pattern where two people 302, 304 both have a relationship308, 310 with a common artifact 306 and have a direct coordination link(i.e., path length of one) 312. In one embodiment, the method and systemof the present disclosure utilizes graph theory, analyzes the componentsof the work product, and analyzes and identifies the importancemeasurements of the links. The components of the work product refers towhat is output by tasks, that is, units of work that produce those workproducts. For example work products may include documents of differenttype such as requirement specifications, design models, code, etc. Tasksrefer to activities such as testing, coding, etc. Thus the presentmethod and system of the present disclosure in one embodiment focuses onand analyzes different kinds of information, other than with respect tothe people who look at tasks. Typically, the components of the workproduct, their relationships and their attributes are “physical”objects, for example, documents that exist persistently and are kept insome repository, and therefore, are easily accessible. Thus, using workcomponents for analysis rather than tasks may provide more accurateresults since the tasks are events that may or may not be recordedcorrectly, depending on the tools and the practices used by theorganization that undertakes them, and since it may be more difficult toexhaustively keep track of the tasks that have produced those objects.

FIG. 4 illustrates indirect coordination having path length two withrespect to a single artifact. When two people are both assigned to thesame work artifact, it is expected that they coordinate in theircommunications. If this does not occur directly, it may be accomplishedthrough an intermediary. FIG. 4 shows an example of a pattern where twopeople 402, 404 both have a relationship 410, 412 with a common artifact408, and have an indirect coordination link of path length two 414 and416 via another person 406.

FIG. 5 illustrates indirect coordination having path length tree withrespect to a single artifact. When two people are both assigned to thesame work artifact, they are expected to coordinate in theircommunications. If this does not occur directly, it may be accomplishedthrough a series of connected intermediaries. FIG. 5 shows an example ofa pattern where two people 502, 504 both have a relationship 508, 510with a common artifact 506, and have an indirect coordination link ofpath length three 512, 514, and 516.

FIGS. 2-5 illustrate examples of the “node tie” reference pattern. Forexample, when two or more people are each involved with a commonartifact, the method and system of the present disclosure expect toobserve “coordination” via a communication link. This coordination isreferred to as collaboration. It is possible to have longer pathlengths, for example, 4, 5, 6, etc. up to the length equal to number ofpeople in the graph P minus one. For example, the longest path length,without repeating nodes, in a network is the number of nodes minus one.FIG. 12 illustrates an example set of reference patterns. Collaborationpatterns 1204, 1206, 1208 may exist between people nodes working on acommon artifact directly or indirectly via one or multiple paths. Notethat anti-patterns are indicated when the dotted line is absent.

FIG. 6 illustrates singular coordination with respect to dependentartifacts. Suppose work artifact s(r) has a dependency on work artifacts(q). Furthermore, suppose that person p has an assigned role withartifact s(r), but no relationships with anyone who has an assigned rolewith work artifact s(q). Then it is expected that person p has someassigned role to artifact s(q), so that p would have detailed workingknowledge of the dependency of s(r) on s(q). FIG. 6 shows an example ofa pattern where one person 602 has a relationship 608, 610 with twoartifacts 604, 606 where one is dependent on the other shown by link612.

FIG. 7 illustrates direct coordination with respect to dependentartifacts. Suppose work artifact s(r) has a dependency on work artifacts(q). Furthermore, suppose that person p(i) has an assigned role withartifact s(r), but no assigned role with s(q). Person p(j), however,does have an assigned role with artifact s(q). Then it is expected thatpersons p(i) and p(j) to have a working relationship so that they arecoordinated. FIG. 7 shows an example of a pattern where two people 702,704 each have a relationship 712, 714 respectively, with an artifact706, 708 respectively, where the artifacts 706, 708 which share a direct(i.e., path length one) dependency 710. Expected relationship betweenthe two persons 702, 704 is shown by the link at 716.

FIG. 8 illustrates indirect coordination, path length two, with respectto dependent artifacts. When two people are assigned to artifacts thatshare a dependency, it is expected that the two people to be coordinatedin their communications. If this does not occur directly, it may beaccomplished through an intermediary. FIG. 8 shows an example of apattern where two people 802, 804 each have a relationship with anartifact 806, 808 respectively, where the artifacts 806, 808 aredistinct but are independent and the people have an indirect (i.e. pathlength two) relationship 816, 818.

FIG. 9 illustrates indirect coordination, path length three, withrespect to dependent artifacts. The example pattern shows two people902, 904 having relationship 910, 912 respectively with an artifact 906,908 respectively, where the artifacts 906, 908 share an indirect (i.e.,path length three) dependency 914. Expected relationship between the twopersons 902, 904 is shown by the links at 916, 918, and 920.

FIGS. 6-9 illustrate examples of the “arc mirroring” reference pattern.For example, when two or more people are each involved with a differentartifact and there is a dependency between the artifacts, the method andsystem of the present disclosure expect to observe “coordination” via acommunication link also between the people. This network of coordinationis referred to as coordination patterns In addition to the examplesshown, there may exist path lengths of greater than three between pairsof people, for instance, up to the length equal to number of people inthe graph P minus one. Without repeating nodes, the longest path lengthin a network is the number of nodes minus one. FIG. 12 illustrates anexample set of reference patterns. Coordination patterns 1212, 1214,1216 may exist between people nodes working on related softwareartifacts directly or indirectly via one or multiple paths.

Node tie collaboration consistency refers to a case whenever a pair ofindividuals (people) both have a relationship with a work artifact, thenone expects to see a path between the people in the social network. Thiscan be expressed conceptually as follows. Define Γ_(s)(G_(S), G_(P),J, 1) to be the number of times that there exist s₀∈S and p_(i),P_(j)∈P, with i≠j, such that (p_(i), s₀), (p_(j), s₀)∈J. For any naturalnumber k>=2, let Γ_(s)(G_(S), G_(P), J, k) denote the number of timesthat there exist s₀∈S and p_(i), p_(j)∈P, with i≠j, such that (p_(i),s₀), (p_(j), s₀)∈J and there is no geodesic (i.e. a shortest pathbetween a pair of nodes, where the path length is measured by the numberof links) from p_(i) to p_(j) of length less than or equal to k−1.Similarly, define Λ_(s)(G_(S), G_(P), J, 1) is defined to be the numberof times that there exist s₀∈S and p_(i), p_(j)∈P, with i≠j, such that(p_(i), s₀), (p_(j), s₀)∈J and (p_(i), p_(j))∈E_(P). For k>−2, letΛ_(s)(G_(S), G_(P), J, k) denote the number of times that there exists₀∈S and p_(i), p_(j)∈P, with i≠j, such that (p_(i), s₀), (p_(j), s₀)∈Jand there is a geodesic from p_(i) to p_(j) of length less than or equalto k. Then for all nonzero natural numbers k, define the k-pathcollaboration (on a single artifact) pattern consistency by the ratio

$\rho_{s,k}\text{:}{= \frac{\Lambda_{s}\left( {G_{S},G_{P},J,k} \right)}{\Gamma_{s}\left( {G_{S},G_{P},J,k} \right)}.}$

Define ρ_(s,0):=0.

Arc mirroring coordination consistency refers to the following: if workartifact s_(r) has a dependency on work artifact s_(q), then one expectsperson p_(j) to be connected to artifact s_(q) either directly or via apath in the people graph by Gp(P,Ep). This concept can be expressedformally as follows. Define Γ_(d)(G_(S), G_(P), J, 0) to be the numberof times that there exist s_(q), s_(r)∈S, q≠r, and p_(j)∈P such that(s_(q), s_(r))∈A_(S) and (p_(j), s_(r))∈J. Define Γ_(d)(G_(S), G_(P),J, 1) to be the number of times that there exist s_(q), s_(r)∈S, q≠r,and p_(i), p_(j)∈P, i≠j, such that (s_(q), s_(r))∈A_(S) and (p_(i),s_(q)), (p_(j), s_(r))∈J. For any natural number k>=2, let Γ_(d)(G_(S),G_(P), J, k) denote the number of times that there exist s_(q), s_(r)∈S,q≠r, and p_(i), p_(j)∈P, i≠j, such that (s_(q), s_(r))∈A_(S) and (p_(i),s_(q)), (p_(j), s_(r))∈J and there is no geodesic from p_(i), to p_(j)of length less than or equal to k−1.

Similarly, define Λ_(d)(G_(S), G_(P), J, 0) to be the number of timesthat there exist s_(q), s_(r)∈S, q≠r, and p_(j)∈P such that (s_(q),s_(r))∈A_(S) and (p_(j), s_(r))∈J. Define Λ_(d)(G_(S), G_(P), J, 1) tobe the number of times that there exist s_(q), s_(r)∈S, q≠r, and p_(i),p_(j)∈P, i≠j, such that (s_(q), s_(r))∈A_(S) and (p_(i), s_(q)), (p_(j),s_(r))∈J and p_(i), p_(j)∈Ep. For k>=2, let Λ_(d)(G_(S), G_(P), J, k)denote the number of times that there exist s_(q), s_(r)∈S, q≠r, andp_(i), p_(j)∈P, i≠j, such that (s_(q), s_(r))∈A_(S) and (p_(i), s_(q)),(p_(j), s_(r))∈J and there is a geodesic from p_(i), to p_(j) of lengthk. Then for all nonzero natural number k, define the k-path coordination(on a pair of dependent artifacts) pattern consistency by the ratio

${\rho_{d,k}\text{:}} = {\frac{\Lambda_{d}\left( {G_{S},G_{P},J,k} \right)}{\Gamma_{d}\left( {G_{S},G_{P},J,k} \right)}.}$

Note that ρ_(l,k) (i.e., ρ_(d,k) where d is equal to 1) is equivalent tothe value of the “congruence” metric in Cataldo et al. under certainassumptions.

The method and system also may aggregate the individual patternconsistency metrics ρ_(s,k) and ρ_(d,k) into organizational consistencymetrics Ω_(s) and Ω_(d). Observe that for any given socio-technicalnetwork with a people node set of size n, the maximum length of any pathin the people graph Gp(P, Ep) is given by n−1. Therefore, the patternconsistency metrics ρ_(s,k) and ρ_(d,k) only make sense for k=0, 1, 2, .. . , n−1. Let {λ_(k), k=0, 1, 2, . . . , n−1} be any finite,nonnegative, non-increasing sequence such that

${\sum\limits_{k = 1}^{n - 1}\lambda_{k}} = 1.$

Then organizational collaboration consistency (node tie) metric may bedefined in the following way:

$\Omega_{s}:={\rho_{s,1} + {\sum\limits_{k = 2}^{n - 1}{\lambda_{k}\rho_{s,k}{\prod\limits_{j = 1}^{k - 2}\; {\left( {1 - \rho_{s,j}} \right).}}}}}$

Likewise, organization coordination consistency (arc mirroring) metricmay be defined as follows:

$\Omega_{d}:={\rho_{d,1} + {\sum\limits_{k = 2}^{n - 1}{\lambda_{k}\rho_{d,k}{\prod\limits_{j = 1}^{k - 1}\; {\left( {1 - \rho_{d,j}} \right).}}}}}$

EXAMPLES

Geometric series: Let 0<r<1 and define λ_(k):=cr^(k), where

$c:={\frac{1 - r}{1 - r^{n}}.}$

Power series: For any natural number p=1, 2, . . . , let

$H:={\sum\limits_{k = 0}^{n - 1}\frac{1}{\left( {k + 1} \right)^{p}}}$

and define

$\lambda_{k}:={\frac{1}{{H\left( {K + 1} \right)}^{p}}.}$

Function-based series: Let ƒ:[0,∞)→(0,∞) be a decreasing function. Let

$c:={\sum\limits_{k = 0}^{n - 1}{f(k)}}$

and define

$\lambda_{k}:={\frac{f(k)}{c}.}$

Then one may choose a specific function ƒ according to specificrequirements. For example, one may choose ƒ(x)=e^(−zx) ² , where z>0 isany positive rational parameter.

The choice of the parameters r (geometric series), p (power series) or z(exponential function based series) may affect how quickly theorganizational consistency parameters λ_(k) tend to zero. This choicemay also affect how much weight is given to the first patternconsistency metric ρ_(*,l) (here * represents either s or d).

Recommended default parameters are r=0.75, p=1 and z=0.05. These defaultsettings yield similar results in the combined organizationalconsistency metrics for each choice of series type.

FIG. 10 illustrates a method in one embodiment of the present disclosurefor finding measurements related to collaboration patterns. At 1002,initialization takes place. For example, counter variables for expectedcollaboration pattern (denominator in a ratio expression) and observedpattern (numerator in the ratio expression) are initialized, variablesfor counting gaps are initialized, and all shortest paths are computed.At 1004, for each artifact and for each unique pair of people nodesjoined to the artifact, a counter for the expected collaboration patternis incremented. If a path of k exists between the people nodes,appropriate path counter is incremented, otherwise the gap counter forthe link is incremented. At 1006, the remaining denominators arecomputed, for example, recursively, and consistency ratios are computediteratively. At 1008, the results are presented.

The following illustrates an algorithm in one embodiment that finds allconsistency ratios, ρ_(s,k), in which δ_(s,k) represents expectedcollaboration pattern and λ_(s,k) represents observed collaborationpattern:

Step 1: For k=1,...,n_(p)−1 (where n_(p)−1 is the maximum geodesic in anetwork with n_(p) nodes, where n_(p) represents the number of people inthe socio technical system being considered):     { Set δ_(s,k) = 0 andλ_(s,k)=0 } Step 2: Precompute all node to node geodesic distances:    gdes(p_(i),p_(j)) for all p_(i) , p_(j) ε P Step 3:   For eachvertex s₀ ε S:     {     Let J_(s0)=the set of all joins from set Jincident on vertex s₀.     For each unique pair in J_(s0) ,     i.e.(p_(i), s₀) , (p_(j), s₀) ε J_(s0) where p_(i) ≠p_(j):       {       Setδ_(s,1) = δ_(s,1) + 1       Set v = gdes(p_(i),p_(j))       If (v < + ∞)        { λ _(s,v)= λ _(s,v) +1 }       else         { a gap isidentified at (p_(i), p_(j)). }       }     } Step 4: Forh=2,...,n_(p)−1:       { Set δ_(s,h) = δ_(s,h−1) − λ _(s,h−1) } Step 5:For k=1,...,n_(p)−1:       { Set ρ_(s,k) = λ _(s,k) / δ_(s,k) } End

The above algorithm simultaneously computes all k-path collaborationpattern consistency ratios, and identifies gaps. Since the maximum pathlength in a network with n_(p) nodes is n_(p-1), it starts byinitializing to zero the counters used to find the denominator andnumerator values respectively. The 2^(nd) step finds all point to pointgeodesic (shortest path based on number of links) values. This step canbe accomplished by iterating a standard shortest path algorithm such asthose known by Dijkstra, or Floyd Warshall. Step 3 iterates byconsidering each artifact node and all of the joins (i.e., linksemanating from the people nodes into the artifact nodes) that connect toit. For each unique pair of joins linked into a common artifact, thealgorithm looks to see if there are two distinct individuals at theother ends of the join pair, and if there is, the denominator isincremented. If there is also a path between these two distinctindividuals, then the appropriate numerator counter is incremented.During the main step, whenever there is no path between a pair of nodesfor which the method and system expect to see communication, a gap isnoted. These gaps are useful to derive the importance values of theindividual links—i.e. how much the overall collaboration would beimproved by adding the link. After step 3, step 4 computes the remainingdenominator values by recursion. This works because, between any pair ofnodes, if there is a path, it is either of length 1, 2, . . . , orn_(p-1) in length. In step 5, the ratios are computed—that is, thenumber of observed patterns are divided by the number of patternsexpected for perfect collaboration interaction.

FIG. 11 illustrates a method in one embodiment for finding measurementsrelated to coordination patterns. At 1102, counter variables areinitialized for expected and observed coordination patterns, and fordetermining gaps. All shortest paths between nodes in the people networkare computed. At 1104, for each unique pair of people nodes joined toadjacent artifacts or linked artifacts, increment the denominator(number of expected coordination in this example). If a path of k existsbetween the people nodes, increment the appropriate path counter(observed coordination pattern), otherwise increment the gap counter forthe link. At 1106, the remaining denominators are computed, e.g.,recursively, and the corresponding consistency ratios are iterativelycomputed. At 1108, the results are presented.

The following illustrates an algorithm in one embodiment that finds allconsistency ratios, ρ_(d,k), in which δ_(d,k) represents expectedcoordination pattern and λ_(d,k) represents observed coordinationpattern:

Step 1: For k=1,...,n_(p)−1 :     { Set δ_(d,k) = 0 and λ _(d,k)=0 }Step 2: Precompute all node to node geodesic distances:    gdes(p_(i),p_(j)) for all p_(i) , p_(j) ε P Step 3:   For each link(s₀ , s₁) ε A_(s):     {     Let J_(s0)=the set of all joins from set Jincident on vertex s₀.     Let J_(s1)=the set of all joins from set Jincident on vertex s₁.     For each unique pair in J_(s0) × J_(s1),    i.e. (p_(i), s₀) , (p_(j), s₁) ε J_(s0) where p_(i) ≠p_(j):       {      Set δ_(d,1) = δ_(d,1)+1       Set v = gdes(p_(i),p_(j))       If(v < + ∞)         { λ _(d,v)= λ _(d,v) +1 }       else         { a gapis identified at (p_(i), p_(j)) }       }     } Step 4: Forh=2,...,n_(p)−1:     { Set δ_(d,h) = δ_(d,h−1) − λ _(d,h−1) } Step 5:For k=1,...,n_(p)−1 :     { Set ρ_(d,k) = λ _(d,k) / δ_(d,k) } End

The algorithm above works in the similar way as the previous algorithm,except that in step 3 step, it iterates by considering each link betweenpairs of software artifact nodes and then each unique pair of joinswhere one is connected to one of the software artifact nodes and one tothe other. Both algorithms perform in polynomial time.

As described above, consistency is measured between conceptual planes inthe socio-technical system. For example, in FIG. 1, consistency may bemeasure between the planes 102 and 104. Each plane comprises acollection of relationships, or links, between nodes or components, orpeople or objects. Consistency does not necessarily mean matching. Thatis, consistency does not necessarily mean that the networks or theplanes are identical in structure. Two or more networks can beconsistent while not matching exactly. For instance, one plane may bemuch larger and denser than the other, and they still may be consistent.

The following illustrates a way to derive link importance measurementsfor links. Links that are not in the graph are also referred to aspotential links in the present disclosure. These links may includebetween people, artifacts, or new joins, or any other links between andamong components of socio-technical system being considered. Linkimportance measurements are also referred to as scores, that is, thedegree to which a link or a potential link contributes to the overallconsistency measurement. The determined scores then may be ordered toprovide a ranking among the links.

Path collaboration (on a single artifact) pattern consistency and thek-path coordination (on a pair of dependent artifacts) patternconsistency (for example, each mathematically described by the ratiosdefined, as well as computationally described by the algorithms, above)provide measurements, both in their individual and weightedcombinations, that are attributes of the socio-technical system as awhole. Each measurement may take on a value between zero and one, andcan be interpreted as a degree to which the socio-technical system isconsistent. That is, a value of zero indicates no consistency, a valueof one indicates complete consistency, and a value of u where 0<u<1(i.e. u is greater than zero as well as less than one) can beinterpreted as the percentage of consistency achieved. For instance, asocio-technical system can be considered to have a socio part comprisingpeople and technical part comprising objects, although not limited tosuch, and consistency may be considered as a measurement relative to thecomparison of the parts. It is also possible to have a socio-technicalsystem with additional parts.

For some socio technical systems, a higher consistency measurement(e.g., close to or equal to the value of one) may be considered betterthan a lower measurement. For example, in an organization working on acommon set of goals, high degree of communication or relationship may beconsidered valuable to the workings of the organization. In othersocio-technical systems, a lower measurement (e.g., close to or equal tothe value of zero) may be considered more desirable. For example,consider a supply chain used to create IEDs (improvised explosivedevices) by a group of terrorists. This may be modeled as asocio-technical system, in which it is preferred to see or drive thesystem to a low consistency measurement, signifying disruption in theeffort.

Related to each component link is a value, referred in this disclosureas a “score” or “importance value,” which measures the contribution bythe link to the overall consistency. Note that a component link's scoremay be influenced by its inclusion (or not) in observed referencepatterns. For example, a score may be higher if a component link isobserved to connect two people who both happen to work on more than oneof the same artifacts. A score may also be higher on a link between twopeople who happen to work on many different artifacts where thedifferent artifacts have a number of dependencies between them.

In one embodiment, a score given to a component link may be derived bycomputing a system-wide consistency measurement twice: once with andonce without the link. On the other hand, general analytical forms forthe score of a component link (be it a component link between people, alink between software artifacts, or a link joining a person and anartifact, or any other joins) can be written in terms of the samenotation given above. For example, the following derives several viewsof importance measurements (or scores) for the different types of linksin one embodiment of the present disclosure. The derivations describedbelow is shown as examples only. Other derivation methods may be used.

The following describes the importance or impact of introducing a linkbetween people in a social-technical network in detail in oneembodiment. Suppose that i≠j and (p_(i), p_(j))∉E_(P). One may sociallyengineer the socio-technical network by introducing person p_(i) andp_(j) to one another. This corresponds to adjoining edge (p_(i), p_(j))to the people graph G_(P). Let G_(P)(p_(i), p_(j)) be the graph obtainedby adjoining edge (p_(i), p_(j)) to G_(P). It is desired to measure theimpact that adding edge (p_(i), p_(j)) to G_(P) would have on the 1-pathcollaboration consistency pattern measure ρ_(s,l) and the 1-pathcoordination measure p_(d,l).

Recall that by collaboration consistency the following is meant:whenever a pair of individuals (people) both have a relationship with awork artifact, then one expects to see a path between the people in thesocial network. Recall that Γ_(s)(G_(S), G_(P), J, 1) is defined to bethe number of times that there exist s₀∈S and p_(i), p_(j)∈P, with i≠j,such that (p_(i), s₀), (p_(j), s₀)∈J. Moreover, Λ_(s)(G_(S), G_(P),J, 1) is defined to be the number of times that there exist s₀∈S andp_(i), p_(j)∈P, with i≠j, such that (p_(i), s₀), (p_(j), s₀)∈J and(p_(i), p_(j))∈E_(P). The 1-path collaboration consistency measure isgiven by

$\rho_{s,1}:={\frac{\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)}{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}.}$

Now suppose that there exists s₀∈S such that (p_(i), s₀), (p_(j), s₀)∈J.Then

Γ_(s)(G _(S) ,G _(P)(p _(i) ,p _(j)),J,1=Γ_(s)(G _(S) ,G _(P) ,J,1

and

Λ_(s)(G _(S) ,G _(P)(p _(i) ,p _(j)),J,1)=Λ_(s)(G _(S) ,G _(P) ,J,1)+1.

Therefore the net impact of adding the edge (p_(i), p_(j)) to G_(P) isgiven by

${\frac{{\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)} + 1}{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)} - \frac{\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)}{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}} = {\frac{1}{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}.}$

On the other hand, if (p_(i), p_(j))∉E_(P) and there does not exist s₀∈Ssuch that (p_(i), s₀), (p_(j), s₀)∈J, then

Λ_(s)(G _(S) ,G _(P)(p _(i) ,p _(j)),J,1)=Λ_(s)(G _(S) ,G _(P) ,J,1)

and

Γ_(s)(G _(S) ,G _(P)(p _(i) ,p _(j)),J,1)=Γ_(s)(G _(S) ,G _(P) ,J,1)

so the net impact of adding the edge (p_(i), p_(j)) to G_(P) is 0. Inother words, there is net impact on ρ_(s,l) of adding edge

$\left( {p_{i},p_{j}} \right) = \left\{ \begin{matrix}\frac{1}{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)} \\0\end{matrix} \right.$

if there exists s₀∈S such that (p_(i), s₀), (p_(j), s₀)∈J, 0 otherwise.

Recall that by coordination consistency the following is meant: if workartifact s_(r) has a dependency on work artifact s_(q), and if personp_(j) is connected to artifact s_(r), then one expects person p_(j) tobe connected to artifact s_(q). Recall that δ_(s)(G_(S), G_(P), J, 1) isdefined to be the number of times that there exist s_(q), s_(r)∈S, q≠r,and p_(i), p_(j)∈P, i≠j, such that (s_(q), s_(r))∈A_(S), and (p_(i),s_(q)), (p_(j), s_(r))∈J. Moreover, Λ_(d)(G_(S), G_(P), J, 1) is definedto be the number of times that there exist s_(q), s_(r)∈S, q≠r, andp_(i), p_(j)∈P, i≠j, such that (s_(q), s_(r))∈A_(S) and (p_(i), s_(q)),(p_(j), s_(r))∈J and (p_(i), p_(j))∈E_(P). The 1-path coordinationconsistency measure is given by

$\rho_{d,1}:={\frac{\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)}{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}.}$

Continue to suppose that i≠j and (p_(i), p_(j))∉E_(P). Now consider theimpact that adding edge (p_(i), p_(j)) would now have on the consistencypattern measure ρ_(d,l). As before, let G_(P)(p_(i), p_(j)) be the graphobtained by adjourning edge (p_(i), p_(j)) to G_(P). Now suppose thatthere exist s_(q), s_(r)∈S, q≠r such that (s_(q), s_(r))∈A_(S) and(p_(i), s_(q)), (p_(j), s_(r))∈J. Then Γ_(d)(G_(S), G_(P)(p_(i), p_(j)),J, 1)=Γ_(d)(G_(S), G_(P), J, 1) and Λ_(d)(G_(S), G_(P)(p_(i), p_(j)), J,1)=Λ_(d)(G_(S), G_(P), J, 1)+1. Therefore the net impact of adding theedge (p_(i), p_(j)) to G_(P) is given by

${\frac{{\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)} + 1}{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)} - \frac{\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)}{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}} = {\frac{1}{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}.}$

On the other hand, if (p_(i), p_(j))≠E_(P) and there does not exists_(q), s_(r)∈S, q≠r such that (s_(q), s_(r))∈A_(S) and (p_(i), s_(q)),(p_(j), s_(r))∈J, then Λ_(d)(G_(S), G_(P)(p_(i), p_(j)), J,1)=Λ_(d)(G_(S), G_(P), J, 1) and Γ_(d)(G_(S), G_(P)(p_(i), p_(j)), J,1)=Γ_(d)(G_(S), G_(P), J, 1) so the net impact of adding the edge(p_(i), p_(j)) to G_(P) is 0.

In other words, there is net impact on ρ_(s,l) of adding edge if

$\left( {p_{i},p_{j}} \right) = \left\{ \begin{matrix}\frac{1}{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)} \\0\end{matrix} \right.$

there exists s₀∈S, q≠r such that (s_(q), s_(r))∈A_(S) and (p_(i),s_(q)), (p_(j), s_(r))∈J, 0 otherwise.

The following describes the importance or impact of assigning new joinsin a socio-technical network in detail in one embodiment. Suppose that(p₀, s₀)∉J. One may engineer the socio-technical network by assigningperson p₀ to task s₀. This corresponds to adjoining arc (p₀, s₀) to thejoin set J. Let J(p₀, s₀) be the graph obtained by adjoining arc (p₀,s₀) to J. It is desirable to measure the impact that adding arc (p₀, s₀)to J would have on the 1-path collaboration consistency pattern measureρ_(s,l) and the 1-path coordination consistency measure ρ_(d,l).

Recall that by collaboration consistency the following is meant:whenever a pair of individuals (people) both have a relationship with awork artifact, then one expects to see a path between the people in thesocial network. Recall that Γ_(s)(G_(S), G_(P), J, 1) is defined to bethe number of times there exist s₀∈S and p_(i), p_(j)∈P with i≠j, suchthat (p_(i), s₀), (p_(j), s₀)∈J. Moreover, Λ_(s)(G_(S), G_(P), J, 1) isdefined to be the number of times there exist s₀∈S and p_(i), p_(j)∈Pwith i≠j, such that (p_(i), s₀), (p_(j), s₀)∈J and (p_(i), p_(j))∈E_(P).The 1-path collaboration consistency measure is given by

$\rho_{s,1}:={\frac{\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)}{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}.}$

In the following discussion, it is assumed that there exists p_(i) withp_(i)≠p₀ such that (p_(i), s₀)∈J. This assumption means that everyartifact in the socio-technical network has at least one person assignedto it a priori. For the sake of simplicity, first examine the case thatthere exists a unique p_(i)∈P with p_(i)≠p₀ such that (p_(i), s₀)∈J. Nowsuppose that (p_(i), p₀)∉E_(P).

Then

Γ_(s)(G _(S) ,G _(P) ,J(p ₀ ,s ₀),1)=Γ_(s)(G _(S) ,G _(P) ,J,1)+1

and

Λ_(s)(G _(S) ,G _(P) ,J(p ₀ ,s ₀),1)=Λ_(s)(G _(S) ,G _(P) ,J,1).

Therefore the net impact of adding the arc (p₀, s₀) to J is given by

${\frac{\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)}{{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)} + 1} - \frac{\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)}{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}} = {\frac{- {\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)}}{{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}\left( {{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)} + 1} \right)}.}$

On the other hand, if (p_(i), p₀)∈E_(P), then

Γ_(s)(G _(S) ,G _(P) ,J(p ₀ ,s ₀),1)=Γ_(s)(G _(S) ,G _(P) ,J,1)+1

and

Λ_(s)(G _(S) ,G _(P) ,J(p ₀ ,s ₀),1)=Λ_(s)(G _(S) ,G _(P) ,J,1)+1

so the net impact of adding the arc (p₀, s₀) to J is given by

${\frac{{\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)} + 1}{{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)} + 1} - \frac{\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)}{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}} = {\frac{{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)} - {\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)}}{{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}\left( {{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)} + 1} \right)}.}$

In other words, there is net impact on ρ_(s,l) of adding arc

$\left( {p_{0},s_{0}} \right) = \left\{ \begin{matrix}\frac{- {\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)}}{{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}\left( {{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)} + 1} \right)} & {{{if}\mspace{11mu} \left( {p_{i},p_{0}} \right)} \notin E_{P}} \\\frac{{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)} - {\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)}}{{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}\left( {{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)} + 1} \right)} & {{{if}\mspace{11mu} \left( {p_{i},p_{0}} \right)} \in {E_{P}.}}\end{matrix} \right.$

The assumption on the uniqueness of p_(i) is not realistic. Let g denotethe number of distinct people p_(i) such that p_(i)≠p₀ and (p_(i),s₀)∈J. Let l denote the number of those distinct people p_(i) such thatp_(i)≠p₀, (p_(i), s₀)∈J and (p_(i), s₀)∈E_(P). Then there is net impacton ρ_(s,l) of adding arc

$\left( {p_{0},s_{0}} \right) = {\frac{{l\; {\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}} - {g\; {\Lambda_{s}\left( {G_{S},G_{P},J,1} \right)}}}{{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)}\left( {{\Gamma_{s}\left( {G_{S},G_{P},J,1} \right)} + g} \right)}.}$

Recall that by coordination consistency meant the following: if workartifact s_(r) has a dependency on work artifact s_(q), and if personp_(j) is connected to artifact s_(r), then one expects person p_(j) tobe connected to artifact s_(q). Recall that Γ_(d)(G_(S), G_(P), J, 1) isdefined to be the number of times that there exist s_(q), s_(r)∈S, q≠r,and p_(i), p_(j)∈P, i≠j, such that (s_(q), s_(r))∈A_(S) and (p_(i),s_(q)), (p_(j), s_(r))∈J. Moreover, Λ_(d)(G_(S), G_(P), J, 1) is definedto be the number of times that there exist s_(q), s_(r)∈S, q≠r, andp_(i), p_(j)∈P, i≠j, such that (s_(q), s_(r))∈A_(S) and (p_(i), s_(q)),(p_(j), s_(r))∈J and (p_(i), p_(j))∈E_(P). The 1-path coordinationconsistency measure is given by

$\rho_{d,1}:={\frac{\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)}{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}.}$

Now assume that there exists s_(q)∈S with s_(q)≠s₀ such that either(s_(q), s₀)∈A_(S) or (s₀, s_(q))∈A_(S). This assumption means that s₀ isnot an isolated software artifact. Moreover, it is assumed that thereexists p_(i)∈P with p_(i)≠p₀ such that (p_(i), s_(q))∈J. This assumptionmeans that every artifact in the socio-technical network has at leastone person other than p₀ assigned to it a priori. In the case thateither of these assumptions does not hold, simply define the net impactof the addition of arc (p₀, s₀) to be 0.

For the sake of simplicity, first examine the case that there exists aunique p_(i)∈P with p_(i)≠p₀ such that (p_(i), s_(q))∈J. Now supposethat (p_(i), p₀)∈E_(P). Then

Γ_(d)(G _(S) ,G _(P) ,J(p ₀ ,s ₀),1)=Γ_(d)(G _(S) ,G _(P) ,J,1)+1

and

Λ_(d)(G _(S) ,G _(P) ,J(p ₀ ,s ₀),1)=Λ_(d)(G _(S) ,G _(P) ,J,1).

Therefore the net impact of adding the arc (p₀, s₀) to J is given by

${\frac{\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)}{{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)} + 1} - \frac{\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)}{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}} = {\frac{- {\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)}}{{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}\left( {{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)} + 1} \right)}.}$

On the other hand, if (p_(i), p₀)∈E_(P), then

Γ_(d)(G _(S) ,G _(P) ,J(p ₀ ,s ₀),1)=Γ_(d)(G _(S) ,G _(P) ,J,1)+1

and

Λ_(d)(G _(S) ,G _(P) ,J(p ₀ ,s ₀),1)=Λ_(d)(G _(S) ,G _(P) ,J,1)+1

so the net impact of adding the are (p₀, s₀) to J is given by

${\frac{{\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)} + 1}{{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)} + 1} - \frac{\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)}{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}} = {\frac{{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)} - {\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)}}{{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}\left( {{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)} + 1} \right)}.}$

In other words, there is net impact on p_(d,l) of adding arc

$\left( {p_{0},s_{0}} \right) = \left\{ \begin{matrix}\frac{- {\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)}}{{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}\left( {{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)} + 1} \right)} & \begin{matrix}{{{if}\mspace{14mu} {\exists{s_{q} \in S}}},{{s_{q} \neq {s_{0}\mspace{14mu} {such}\mspace{14mu} {that}\mspace{11mu} \left( {s_{q},s_{0}} \right)}} \in {A_{S}\mspace{14mu} {or}\mspace{11mu} \left( {s_{0},s_{q}} \right)} \in A_{S}}} \\{{{and}\mspace{14mu} {\exists{!{p_{i} \in P}}}},{{p_{i} \neq {p_{0}\mspace{14mu} {so}\mspace{14mu} {that}\mspace{11mu} \left( {p_{i},s_{q}} \right)}} \in {J\mspace{14mu} {and}\mspace{14mu} \left( {p_{i},p_{0}} \right)} \notin E_{P}},}\end{matrix} \\\frac{{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)} - {\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)}}{{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}\left( {{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)} + 1} \right)} & \begin{matrix}{{{if}\mspace{14mu} {\exists{s_{q} \in S}}},{{s_{q} \neq {s_{0}\mspace{14mu} {such}\mspace{14mu} {that}\mspace{11mu} \left( {s_{q},s_{0}} \right)}} \in {A_{S}\mspace{14mu} {or}\mspace{11mu} \left( {s_{0},s_{q}} \right)} \in A_{S}}} \\{{{and}\mspace{14mu} {\exists{!{p_{i} \in P}}}},{{p_{i} \neq {p_{0}\mspace{14mu} {so}\mspace{14mu} {that}\mspace{11mu} \left( {p_{i},s_{q}} \right)}} \in {J\mspace{14mu} {and}\mspace{11mu} \left( {p_{i},p_{0}} \right)} \notin E_{P}},}\end{matrix} \\0 & \begin{matrix}{{{if}\mspace{14mu} {\forall{s_{q} \in S}}},\left( {s_{q},s_{0}} \right),{\left( {s_{0},s_{q}} \right) \notin A_{S}},} \\{{{if}\mspace{14mu} {\exists{s_{q} \in S}}},{{s_{q} \neq {s_{0}\mspace{14mu} {such}\mspace{14mu} {that}\mspace{11mu} \left( {s_{q},s_{0}} \right)}} \in {A_{S}\mspace{14mu} {or}\mspace{11mu} \left( {s_{0},s_{q}} \right)} \in A_{S}}}\end{matrix} \\0 & {{{but}\mspace{14mu} {\forall{p_{i} \in P}}},{{{either}\mspace{14mu} p_{i}} = {{p_{0}\mspace{14mu} {or}\mspace{11mu} \left( {p_{i},s_{q}} \right)} \neq {J.}}}}\end{matrix} \right.$

The assumption on the uniqueness of p_(i) is not realistic. Let g denotethe number of distinct people p_(i) such that p_(i)≠p₀ and (p_(i),s_(q))∈J. Let l denote the number of those distinct people p_(i) suchthat p_(i)≠p₀, (p_(i), s_(q))∈J, and (p_(i), p₀)∈E_(P). Then there isnet impact on p_(d,l) of adding arc

$\left( {p_{0},s_{0}} \right) = \left\{ \begin{matrix}\frac{{l\; {\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}} - {g\; {\Lambda_{d}\left( {G_{S},G_{P},J,1} \right)}}}{{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)}\left( {{\Gamma_{d}\left( {G_{S},G_{P},J,1} \right)} + g} \right)} & \begin{matrix}{{{if}\mspace{14mu} {\exists{s_{q} \in S}}},{{s_{q} \neq {s_{0}\mspace{14mu} {such}\mspace{14mu} {that}\mspace{11mu} \left( {s_{q},s_{0}} \right)}} \in {A_{S}\mspace{14mu} {or}\mspace{14mu} \left( {s_{0},s_{q}} \right)} \in A_{S}}} \\{{{and}\mspace{14mu} {\exists{p_{i} \in P}}},{{p_{i} \neq {p_{0}\mspace{14mu} {so}\mspace{14mu} {that}\mspace{11mu} \left( {p_{i},s_{q}} \right)}} \in J}}\end{matrix} \\0 & \begin{matrix}{{{if}\mspace{14mu} {\forall{s_{q} \in S}}},\left( {s_{q},s_{0}} \right),{\left( {s_{0},s_{q}} \right) \notin A_{S}},} \\{{{if}\mspace{14mu} {\exists{s_{q} \in S}}},{{s_{q} \neq {s_{0}\mspace{14mu} {such}\mspace{14mu} {that}\mspace{11mu} \left( {s_{q},s_{0}} \right)}} \in {A_{S}\mspace{14mu} {or}\mspace{11mu} \left( {s_{0},s_{q}} \right)} \in A_{S}}}\end{matrix} \\0 & {{{but}\mspace{14mu} {\forall{p_{i} \in P}}},{{{either}\mspace{14mu} p_{i}} = {{p_{0}\mspace{14mu} {or}\mspace{11mu} \left( {p_{i},s_{q}} \right)} \notin {J.}}}}\end{matrix} \right.$

Once a score for all component links have been established using aprocess such as the one described above, then each component link canalso be assigned a ranking, for example, by ordering either in ascendingor descending order, depending on the application. As an example, thelist of component links and their scores may be sorted into descendingorder. The component link with the largest score is given the rank of 1,the next highest is given rank 2, and so on. Component links withidentical (i.e. tied) scores may be assigned the same (equal) rank. Astep in the ranking may or may not be skipped when there are rankingties.

Different from the weights considered to combine consistencymeasurements, described in the equations previously, there may beweights assigned to component links and nodes that are used incomputations of the component link scores. These weights may beassociated with attributes of the component links and nodes. Forexample, a component node that represents a software artifact may havean associated complexity measurement, such as “cyclomatic complexity”developed by Thomas McCabe (reference IEEE Transactions On SoftwareEngineering, Vol. SE-2, No. 4, December 1976, pp 308-320 by ThomasMcCabe). Many other examples of complexity metrics, general metrics, andother attributes exist. These node attributes may be considered asweights that impact the scores. For example, if a component linkconnects two people who both happen to work on the same artifact and theartifact happens to have a higher weight, then the component link scoremay be bumped up proportionally, for example, considering the value ofthe weight in the overall collection of weights.

The method and system of the present disclosure in one embodimentprovides mechanism for quantifying alignments or gaps between workinggroups and their work product and/or any other work factors. Thequantification can be used to re-align the work group structure and/orthe work product structure, for example, to improve an overall outcome,for instance, for more productive collaborative development.

While the examples shown above were related to socio-technical graphsinvolving software development, the method and system may be applied inany other development and design project, including but not limited tohardware, system, manufacturing, etc. Further, the method and system ofthe present disclosure may be used in general graph comparison, notlimited to socio-technical graphs.

The system and method of the present disclosure may be implemented andrun on a general-purpose computer or computer system. The computersystem may be any type of known or will be known systems and maytypically include a processor, memory device, a storage device,input/output devices, internal buses, and/or a communications interfacefor communicating with other computer systems in conjunction withcommunication hardware and software, etc.

The terms “computer system” and “computer network” as may be used in thepresent application may include a variety of combinations of fixedand/or portable computer hardware, software, peripherals, and storagedevices. The computer system may include a plurality of individualcomponents that are networked or otherwise linked to performcollaboratively, or may include one or more stand-alone components. Thehardware and software components of the computer system of the presentapplication may include and may be included within fixed and portabledevices such as desktop, laptop, server.

The embodiments described above are illustrative examples and it shouldnot be construed that the present invention is limited to theseparticular embodiments. Thus, various changes and modifications may beeffected by one skilled in the art without departing from the spirit orscope of the invention as defined in the appended claims.

1. A computer implemented method of scoring a plurality of componentlinks in a socio technical system having a plurality of componentsrepresenting people and objects, the plurality of components linksrepresenting a plurality of relationships between the plurality ofcomponents, comprising: determining a measure of consistency relative toa network of people components and a network of object components in asocio technical system, the network of people components includingcomponents representing people and one or more links between thecomponents representing people, and the network of object componentsincluding components representing objects worked on by at least some ofthe components representing people and one or more links between thecomponents representing objects; and determining a measure ofcontribution to the measure of consistency for one or more links betweensaid components, based on presence or absence of said one or more linksin the social technical system, wherein the measure of contribution andthe measure of consistency can be used for analyzing and structuringwork group in a project.
 2. The method of claim 1, wherein the step ofdetermining a measure of consistency includes determining a measure ofconsistency relative to two or more people in the network of peoplecomponents working on a same object in the network of object components.3. The method of claim 1, wherein the step of determining a measure ofconsistency includes determining a measure of consistency relative totwo or more people in the network of people components each working onan object and dependencies between said each object.
 4. The method ofclaim 1, wherein the step of determining a measure of consistencyfurther includes aggregating said measure of consistency determined forall components and component links in the socio-technical system todetermine a system level measure of consistency.
 5. The method of claim1, wherein the step of determining a measure of contribution includes:identifying patterns and anti-patterns within the plurality ofcomponents based on a set of expected patterns in relationships betweenthe plurality of components in the socio technical system; and assigninga measure of contribution to each of said plurality of component linksbased on said identified patterns and anti-patterns.
 6. The method ofclaim 1, further including: identifying a weighing factor for said oneor more links between said components, the weighing factor beingdependent on a degree to which expected links exist; adjusting themeasure of contribution for said one or more links between saidcomponents based on the identified weighing factor.
 7. The method ofclaim 1, further including: identifying a weighing factor for each ofsaid component links, the weighing factor being dependent on anestimation of complexity of joining nodes; adjusting the measure ofcontribution based on the identified weighing factor.
 8. The method ofclaim 1, further including: identifying a weighing factor for each ofsaid component links, the weighing factor being dependent on one or moreattributes of one or more adjoining components; and; adjusting themeasure of contribution based on the identified weighing factor.
 9. Themethod of claim 1, further including: determining the measure ofcontribution for each of the plurality of component links; and rankingthe measure of contribution.
 10. The method of claim 1, furtherincluding: determining a measure of consistency, measure ofcontribution, and rank for one or more subsets of components in thesocio technical network.
 11. The method of claim 1, further including:identifying one or more component link gaps between one or morecomponents; determining an impact of filling said one or more componentlink gaps.
 12. The method of claim 1, further including: identifying oneor more component link gaps between one or more components; determiningan importance factor associated with said one or more component linkgaps.
 13. The method claim 1, wherein the step of determining a measureof consistency includes: identifying expected patterns in relationshipsbetween people components based on relationships between one or moreobject components; observing actual patterns in relationships betweenpeople components; and determining a measure of consistency based onsaid expected patterns and said actual patterns.
 14. A computerimplemented method of determining a score for a plurality of componentlinks in a social technical system having a plurality of componentsrepresenting people and objects, comprising: selecting a component linkfrom a plurality of component links; assigning a score to the selectedlink based on one or more scores of a subset of other links andcomponents; and processing said component link according to the score.15. The method of claim 14, wherein the processing step includes rankingsaid component links according to their scores.
 16. The method of claim14, wherein the processing step includes presenting said component linksaccording to their scores.
 17. The method of claim 14, furtherincluding: generating an initial estimate of a rank for each of thecomponent links; updating the estimate of a rank for each of thecomponent links using analytics derived from a reference pattern, thereference pattern including expected links among the components; andprocessing the component links according to the respective updatedranks.
 18. A system for scoring a plurality of component links in asocio technical system having a plurality of components representingpeople and objects, the plurality of components links representing aplurality of relationships between the plurality of components,comprising: means for determining a measure of consistency relative to anetwork of people components and a network of object components in asocio technical system, the network of people components includingcomponents representing people and one or more links between thecomponents representing people, and the network of object componentsincluding components representing objects worked on by at least some ofthe components representing people and one or more links between thecomponents representing objects; and means for determining a measure ofcontribution to the measure of consistency for one or more links betweensaid components, based on presence or absence of said one or more linksin the social technical system, wherein the measure of contribution andthe measure of consistency can be used for analyzing and structuringwork group in a project.
 19. The system of claim 18, further includingmeans for ordering said measure of contribution determined for theplurality of component links into ranks.
 20. The system of claim 18,wherein the network of people components are represented in a socioplane and the network of object components are represented in atechnical plane of the socio technical system.